Withstanding detector attacks in continuous-variable quantum key distribution via mean-restricted unary linear regression

The distinguishing of coherent states with minimum error is one of the fundamental tasks in continuous-variable quantum key distribution (CV-QKD). Homodyne detector, which is also a common element in current telecommunication, is considered as the simplest setup for such tasks due to it relying only on Gaussian operations. However, a practical homodyne detector has a finite linearity domain, thus eavesdroppers can open secure loopholes by displacing its operation into the nonlinearity domain, e.g., saturation attack and homodyne-detector-blinding attack. Here, we propose a counteracting strategy using mean-restricted unary linear regression to defend against such attacks caused by finite linearity domain problem. This strategy, which relies only on local operations plus classical communication (LOCC) processing, can estimate the displacements from the eavesdropper and then recover the attacked data. To show its practical utility in CV-QKD, we discuss two potential applications under composable security: (1) against saturation attack with one average to limit the line fitted, (2) against homodyne-detector-blinding attack with various averages to limit the line fitted. Numerical analysis shows that the estimated displacements have acceptable accuracy compared with the real displacements caused by the eavesdropper.